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Simplifying 0.95x2 + -15x + 20 = 0 Reorder the terms: 20 + -15x + 0.95x2 = 0 Solving 20 + -15x + 0.95x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.95 the coefficient of the squared term: Divide each side by '0.95'. 21.05263158 + -15.78947368x + x2 = 0 Move the constant term to the right: Add '-21.05263158' to each side of the equation. 21.05263158 + -15.78947368x + -21.05263158 + x2 = 0 + -21.05263158 Reorder the terms: 21.05263158 + -21.05263158 + -15.78947368x + x2 = 0 + -21.05263158 Combine like terms: 21.05263158 + -21.05263158 = 0.00000000 0.00000000 + -15.78947368x + x2 = 0 + -21.05263158 -15.78947368x + x2 = 0 + -21.05263158 Combine like terms: 0 + -21.05263158 = -21.05263158 -15.78947368x + x2 = -21.05263158 The x term is -15.78947368x. Take half its coefficient (-7.89473684). Square it (62.32686977) and add it to both sides. Add '62.32686977' to each side of the equation. -15.78947368x + 62.32686977 + x2 = -21.05263158 + 62.32686977 Reorder the terms: 62.32686977 + -15.78947368x + x2 = -21.05263158 + 62.32686977 Combine like terms: -21.05263158 + 62.32686977 = 41.27423819 62.32686977 + -15.78947368x + x2 = 41.27423819 Factor a perfect square on the left side: (x + -7.89473684)(x + -7.89473684) = 41.27423819 Calculate the square root of the right side: 6.424502953 Break this problem into two subproblems by setting (x + -7.89473684) equal to 6.424502953 and -6.424502953.Subproblem 1
x + -7.89473684 = 6.424502953 Simplifying x + -7.89473684 = 6.424502953 Reorder the terms: -7.89473684 + x = 6.424502953 Solving -7.89473684 + x = 6.424502953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.89473684' to each side of the equation. -7.89473684 + 7.89473684 + x = 6.424502953 + 7.89473684 Combine like terms: -7.89473684 + 7.89473684 = 0.00000000 0.00000000 + x = 6.424502953 + 7.89473684 x = 6.424502953 + 7.89473684 Combine like terms: 6.424502953 + 7.89473684 = 14.319239793 x = 14.319239793 Simplifying x = 14.319239793Subproblem 2
x + -7.89473684 = -6.424502953 Simplifying x + -7.89473684 = -6.424502953 Reorder the terms: -7.89473684 + x = -6.424502953 Solving -7.89473684 + x = -6.424502953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.89473684' to each side of the equation. -7.89473684 + 7.89473684 + x = -6.424502953 + 7.89473684 Combine like terms: -7.89473684 + 7.89473684 = 0.00000000 0.00000000 + x = -6.424502953 + 7.89473684 x = -6.424502953 + 7.89473684 Combine like terms: -6.424502953 + 7.89473684 = 1.470233887 x = 1.470233887 Simplifying x = 1.470233887Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.319239793, 1.470233887}
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